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Mathematical Formalization Specialist (Lean / Formal Proof Systems)
Remote (Global)
$50 – $150/hr
July 14, 2026
Job description
Mathematical Formalization Specialist (Lean / Formal Proof Systems)
About the Role
What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems — especially Lean — to tackle problems that sit beyond the reach of automated tools.
This is a fully remote, flexible contract role at the intersection of mathematics and computer science. You'll work on genuinely hard problems, translating rigorous human arguments into machine-verifiable formalizations that help map the frontier of what proof assistants can express, capture, and automate.
- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: Flexible, task-based
What You'll Do
- Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness
- Analyze proofs across mathematical domains — identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or fail
- Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop clean, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
Sample Work You Might Do
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments
- Investigate where automated provers break down — and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)
- Write Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
Who You Are
Required:
- Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal proof systems — Lean strongly preferred
- Genuine enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
- Ability to translate dense, informal mathematical arguments into clean, structured formal proofs
Nice to Have:
- Familiarity with type theory, the Curry–Howard correspondence, and proof automation tools
- Experience contributing to large-scale formalization projects such as mathlib
- Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
- Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies
The Ideal Candidate
You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant argument and expressing it in a form a machine can understand. You appreciate precision, structural beauty, and the intellectual challenge of resolving gaps that automated tools cannot yet bridge. You don't just do mathematics — you think carefully about how mathematics is done.
Why Join Us
- Work on cutting-edge AI research projects alongside leading research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually stimulating work
- Contribute directly to advancing the reliability and reasoning capabilities of next-generation AI
- Potential for ongoing work and contract extension as new projects launch
Apply now
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